This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380905 #151 Apr 17 2025 09:34:12
%S A380905 3,5,23,7,433,2447,9377,82597,134687
%N A380905 Smallest number k such that k^(2*3^n) - 6 is prime.
%C A380905 Terms must have an ending digit of 3, 5 or 7. If k ends in 1 or 9, then k^(2*3^n)-6 ends in a 5, which is not prime.
%C A380905 a(7) is the first composite term. - _Michael S. Branicky_, Feb 24 2025
%e A380905 For n=0, k^(2*3^0) - 6 is prime for the first time at a(0) = k = 3.
%e A380905 For n=5, k^(2*3^5) - 6 is prime for the first time at a(5) = k = 2447.
%o A380905 (Python)
%o A380905 from sympy import isprime
%o A380905 from itertools import count
%o A380905 def a(n): return next(k for k in count(2) if k%10 in {3,5,7} and isprime(k**(2*3**n)-6))
%o A380905 (PARI) a(n) = my(p=3,q=2*3^n); while (!ispseudoprime(p^q-6), p+=2); p; \\ _Michel Marcus_, Feb 08 2025
%Y A380905 Cf. Subsequence of A382246.
%Y A380905 Cf. A008776, A025192.
%Y A380905 Cf. A028879 (a(0)), A239414 (a(1)) for the first term.
%K A380905 nonn,more,hard
%O A380905 0,1
%A A380905 _Jakub Buczak_, Feb 07 2025
%E A380905 a(7) from _Michael S. Branicky_, Feb 24 2025
%E A380905 a(8) from _Georg Grasegger_, Apr 17 2025